document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33570>Question 33570</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me with this problem i have no idea how to get the answer and i have been working on it for an hour. solve the system of equations.<BR>\n" );
document.write( "3x+4y+z=7<BR>\n" );
document.write( "   2y+z=3<BR>\n" );
document.write( "-5x+3y+8z=-31<BR>\n" );
document.write( "thank you!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #19971 by </B><A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><B>mukhopadhyay(490)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=19971\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sorry to hear that you have been trying this for an hour.  Here it goes:<BR>\n" );
document.write( "There are various ways to solve a system of linear equations.  They are: Elimination method, Substitution method, Cramer's Rule etc.  I would use Cramer's Rule to do this.<BR>\n" );
document.write( "Determinant of the matrix = 3(16-3)-5(4-2) = 29;<BR>\n" );
document.write( "Determinant of X = 7(16-3)-3(32-3)-31(4-2) = 91-87-62 = -58<BR>\n" );
document.write( "Determinant of Y = 3(24+31)-5(7-3) = 165-20 = 145;<BR>\n" );
document.write( "Determinant of Z = 3(-62-9)-5(12-14) = -213+10 = -193;<BR>\n" );
document.write( "x = Determinant of X / Determinant of the matrix = -58/29 = -2;<BR>\n" );
document.write( "y = Determinant of Y / Determinant of the matrix = 145/29 = 5;<BR>\n" );
document.write( "z = Determinant of Z / Determinant of the matrix = -193/29 = -7;<BR>\n" );
document.write( "Answer: (x,y,z) = (-2,5,-7)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );